RUI New Generation of AI-Augmented Quantum Monte Carlo Libraries to Guide the Search for Exotic Superfluid Phases in Cold Atoms

该项目将把成熟的最先进的数值技术与创新的人工智能工具结合起来，计算强关联费米超流体的平衡和动力学性质。在非常活跃的超冷原子领域，这个项目的结果将指导对奇异超流相的实验搜索，例如依赖非传统配对机制的物质的非平凡超流态，或者迷人的拓扑超流的存在。来自该项目的新见解可能会对物理学产生深刻影响，甚至超出冷原子领域，并可能为更深入地理解非常规超导体和核物质中的超流态铺平道路。将开发新的数据分析工具和可视化技术，以捕捉最重要的物理机制。PI计划投入大量努力，使尽可能多的人能够接触到这些方法和主题，并解决教授量子力学的新方法。学生们将能够运行虚拟实验并探索新的物质相，并将有一个独特的机会来学习如何成为未来的科学家。新一代辅助场量子蒙特卡罗技术将被提出：人工智能工具将引导一个自洽的过程，以最大限度地减少由于技术基础的近似造成的偏差。这将通过从量子蒙特卡罗数据中学习的反馈过程中的尝试波函数的优化来实现。该项目有望为费米超流体产生准确的非微扰数据。这项研究将讨论平衡性质，如配对、密度和自旋关联，以及动力学性质，如谱函数和动力学结构因子，它们提供了获得系统低能激发的途径。准确的数值数据将为探测冷原子中新的奇异相这一重大挑战提供实验指导，特别是当自旋-轨道耦合存在时，特别关注自旋极化系统中复杂的交织有序。对这种超流体相背后的物理机制的基本理解也有望取得实质性进展。将讨论自旋极化系统中有限动量库珀对的形成，研究其与密度和自旋有序的相互作用，并结合观察非平凡拓扑性质的可能性，研究自旋-轨道耦合的作用。通过计算动力学关联来研究系统的激发态流形，将使PI可以直接将预测结果与光谱和散射实验相比较，并计算集体模色散，这对于奇特相的实验检测是至关重要的。除了指导实验搜索外，这些结果还将作为多体理论和强关联系统计算方法的有价值的基准，在这些系统中，简单的微扰方法注定会失败。最后，PI计划致力于开发新的可视化工具来捕捉关键的物理机制，预计将创造最佳环境，从本科生开始培训下一代学生、教师和研究人员。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This project will interface well-established state-of-the-art numerical techniques with innovative artificial intelligence tools to compute equilibrium and dynamical properties of strongly correlated Fermi superfluids. In the very active field of ultracold atoms, the results of this project will guide experimental searches for exotic superfluid phases, such as non-trivial superfluid states of matter that rely on unconventional pairing mechanisms or the existence of fascinating topological superfluids. The new insights that will come from this project may have a deep impact in physics, even beyond the field of cold atoms, and may pave the way for a deeper understanding of superfluid states in unconventional superconductors and in nuclear matter. Novel data analysis tools and visualization techniques will be developed to capture the most important physical mechanisms. The PI plans to dedicate substantial effort to make the methods and topics accessible to as many people as possible, and to address novel ways to teach quantum mechanics. Students will be able to run virtual experiments and to explore new phases of matter and will have a unique opportunity to learn how to become the scientists of the future.A new generation of auxiliary-field quantum Monte Carlo techniques will be proposed: artificial intelligence tools will guide a self-consistent procedure to minimize the bias due to the approximations underlying the technique. This will be achieved through the optimization of the trial wave function within a feedback process which learns from the quantum Monte Carlo data. This project is expected to generate accurate non-perturbative data for Fermi superfluids. The study will address both equilibrium properties, like pairing, density and spin correlations, and dynamical properties, like spectral functions and dynamical structure factors, which give access to the low-energy excitations of the systems. The accurate numerical data will provide guidance to the experiments in the major challenge of detecting new exotic phases in cold atoms, with particular focus on complex intertwined orders in spin-polarized systems when spin-orbit coupling is present. Substantial advances in the fundamental understanding of the physical mechanisms underlying such superfluid phases are also expected. The formation of Cooper pairs with finite momentum in spin-polarized systems will be addressed, the interplay with density and spin order will be studied and the role of spin-orbit coupling will be investigated, in connection with the possibility of observing non-trivial topological properties. The study of the manifold of excited states of a system through the calculation of dynamical correlations will allow the PI to directly compare the predictions with spectroscopy and scattering experiments and to compute the dispersion of collective modes, which is crucial for the experimental detection of exotic phases. In addition to guiding experimental searches, the results will also serve as valuable benchmarks for many-body theories and computational methods for strongly correlated systems, where simple perturbative approaches are doomed to fail. Finally, the efforts that the PI plans to dedicate to the development of novel visualization tools to capture the key physical mechanisms are expected to create the best environment to train the next generation of students, teachers and researchers in quantum mechanics, starting from their undergraduate studies.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.